/* linbox/field/gf2.h
 * Copyright (C) 2003-2007 The LinBox group
 *
 * Authors : B. Hovinen, JG Dumas, C. Pernet
 *
 * ------------------------------------
 *
 *
 * ========LICENCE========
 * This file is part of the library LinBox.
 *
 * LinBox is free software: you can redistribute it and/or modify
 * it under the terms of the  GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 * ========LICENCE========
 *.
 */

#ifndef __LINBOX_field_gf2_H
#define __LINBOX_field_gf2_H

#include "linbox/linbox-config.h"
#include <iostream>
#include <climits>
#include <cmath>

#include "linbox/util/debug.h"
#include "linbox/integer.h"
#include "linbox/vector/bit-vector.h"
#include "linbox/field/field-traits.h"
// #include "linbox/vector/vector-domain.h"

#define stdBitReference std::vector<bool>::reference

// Namespace in which all LinBox code resides
namespace LinBox
{

	class GF2RandIter;

        /**
         * \brief Integers modulo 2
         *
         * This is a tuned implementation of the field of integers modulo
         * 2. In particular, when one constructs a VectorDomain object over
         * this field, highly optimized bit operations will be used to make
         * vector arithmetic very fast.
         \ingroup field
        */

	template <class Ring>
	struct ClassifyRing;

	class GF2;

	template<>
	struct ClassifyRing<GF2> {
		typedef RingCategories::ModularTag categoryTag;
	};

	class GF2 {
	public:
		const bool zero,one,mOne;


            /** Element type
             */
		typedef bool Element;
        typedef BitVector::pointer Element_ptr;
        typedef BitVector::const_pointer ConstElement_ptr;
		typedef bool Residu_t;

            /** Random iterator generator type.
             * It must meet the common object interface of random element generators
             * as given in the the archetype RandIterArchetype.
             */
		typedef GF2RandIter RandIter;

            /** @name Object Management
             */
            //@{

            /** Default constructor.
             */
		GF2 () :
                zero(false),one(true),mOne(true)
            {}

		GF2 (int p, int exp = 1) :
                zero(false),one(true),mOne(true)
            {
                if(p != 2) throw PreconditionFailed(LB_FILE_LOC,"modulus must be 2");
                if(exp != 1) throw PreconditionFailed(LB_FILE_LOC,"exponent must be 1");
            }

            /** Copy constructor.
             * Constructs Givaro::Modular object by copying the field.
             * This is required to allow field objects to be passed by value
             * into functions.
             * @param  F Givaro::Modular object.
             */
		GF2 (const GF2 & F ) :
                zero(false),one(true),mOne(true) {
        }

            /** Assignment operator.
             * Required by the archetype
             *
             * @param F constant reference to Givaro::Modular object
             * @return reference to Givaro::Modular object for self
             */
		GF2 &operator = (const GF2 &F)
            {
                return *this;
            }

            /** Initialization of field base element from an integer.
             * Behaves like C++ allocator construct.
             * This function assumes the output field base element x has already been
             * constructed, but that it is not already initialized.
             * This is not a specialization of the template function because
             * such a specialization is not allowed inside the class declaration.
             * @return reference to field base element.
             * @param x field base element to contain output (reference returned).
             * @param y integer.
             */
		Element &init (Element &x, const int64_t &y ) const
            {
                return x = y & 1;
            }

		Element &init (Element &x, const uint64_t &y ) const
            {
                return x = y & 1;
            }

		Element &init (Element &x, const bool &y ) const
            {
                return x = y;
            }
/*
  Element &init (Element &x, const long &y ) const
  {
  return x = y & 1;
  }

  Element &init (Element &x, const unsigned long &y ) const
  {
  return x = y & 1;
  }

  Element &init (Element &x, const float &y) const
  {
  return x = static_cast<unsigned char>(y) & 1;
  }

*/
		Element &init (Element &x, const double &y) const
            {
                return x = static_cast<unsigned char>(y) & 1;
            }

		Element &init (Element &x, const integer &y) const
            {
                    //return x = static_cast<long>(y) & 1;
                return x = y & (uint32_t)1;
            }


		Element &init(Element&x) const
            {
                return x = false;
            }

		BitVector::reference init (BitVector::reference x, const integer &y = 0) const
            {
                return x = y & (uint32_t)1;
            }

		stdBitReference init (stdBitReference x, const integer &y = 0) const
            {
                return x = y & (uint32_t)1;
            }

            /** Conversion of field base element to a template class T.
             * This function assumes the output field base element x has already been
             * constructed, but that it is not already initialized.
             * @return reference to template class T.
             * @param x template class T to contain output (reference returned).
             * @param y constant field base element.
             */
		integer &convert (integer &x, Element y) const
            {
                return x = y;
            }

		stdBitReference convert (stdBitReference x, Element y) const
            {
                return x = y;
            }

		template<class XXX>
		XXX& convert (XXX& x, Element y) const
            {
                return x = static_cast<XXX>(y);
            }

#if 0
		unsigned int &convert (unsigned int &x, Element y) const
            {
                return x = static_cast<unsigned int>(y);
            }

		int &convert (int &x, Element y) const
            {
                return x = static_cast<int>(y);
            }

		unsigned long &convert (unsigned long &x, Element y) const
            {
                return x = static_cast<unsigned long>(y);
            }

		long &convert (long &x, Element y) const
            {
                return x = static_cast<int>(y);
            }

		float &convert (float &x, Element y) const
            {
                return x = static_cast<float>(y);
            }

		double &convert (double &x, Element y) const
            {
                return x = static_cast<double>(y);
            }
#endif

            /** Assignment of one field base element to another.
             * This function assumes both field base elements have already been
             * constructed and initialized.
             * @return reference to x
             * @param  x field base element (reference returned).
             * @param  y field base element.
             */
		Element &assign (Element &x, Element y) const
            {
                return x = y;
            }

		BitVector::reference assign (BitVector::reference x, Element y) const
            {
                return x = y;
            }

		stdBitReference assign (stdBitReference x, Element y) const
            {
                return x = y;
            }

            /** Cardinality.
             * Return integer representing cardinality of the domain.
             * Returns a non-negative integer for all domains with finite
             * cardinality, and returns -1 to signify a domain of infinite
             * cardinality.
             * @return integer representing cardinality of the domain
             */
		integer &cardinality (integer &c) const
            {
                return c = 2;
            }

            /** Characteristic.
             * Return integer representing characteristic of the domain.
             * Returns a positive integer to all domains with finite characteristic,
             * and returns 0 to signify a domain of infinite characteristic.
             * @return integer representing characteristic of the domain.
             */
		integer &characteristic (integer &c) const
            {
                return c = 2;
            }

            //@} Object Management

            /** @name Arithmetic Operations
             * x <- y op z; x <- op y
             * These operations require all elements, including x, to be initialized
             * before the operation is called.  Uninitialized field base elements will
             * give undefined results.
             */
            //@{

            /** Equality of two elements.
             * This function assumes both field base elements have already been
             * constructed and initialized.
             * @return boolean true if equal, false if not.
             * @param  x field base element
             * @param  y field base element
             */
		bool areEqual (Element x, Element y) const
            {
                return x == y;
            }

            /** Zero equality.
             * Test if field base element is equal to zero.
             * This function assumes the field base element has already been
             * constructed and initialized.
             * @return boolean true if equals zero, false if not.
             * @param  x field base element.
             */
		bool isZero (Element x) const
            {
                return !x;
            }

            /** One equality.
             * Test if field base element is equal to one.
             * This function assumes the field base element has already been
             * constructed and initialized.
             * @return boolean true if equals one, false if not.
             * @param  x field base element.
             */
		bool isOne (Element x) const
            {
                return x;
            }

            /** MOne equality.
             * Test if field base element is equal to one.
             * This function assumes the field base element has already been
             * constructed and initialized.
             * @return boolean true if equals one, false if not.
             * @param  x field base element.
             */
		bool isMOne (Element x) const
            {
                return x;
            }

            /** Invertibility.
             * Test if field base element is a unit.
             * This function assumes the field base element has already been
             * constructed and initialized.
             * @return boolean true if is a unit, false if not.
             * @param  x field base element.
             */
		bool isUnit (Element x) const
            {
                return x;
            }

            //@} Arithmetic Operations

            /** @name Input/Output Operations */
            //@{

            /** Print field.
             * @return output stream to which field is written.
             * @param  os  output stream to which field is written.
             */
		std::ostream &write (std::ostream &os) const
            {
                return os << "integers mod 2";
            }

            /** Read field.
             * @return input stream from which field is read.
             * @param  is  input stream from which field is read.
             */
		std::istream &read (std::istream &is)
            {
                return is;
            }

            /** Print field base element.
             * This function assumes the field base element has already been
             * constructed and initialized.
             * @return output stream to which field base element is written.
             * @param  os  output stream to which field base element is written.
             * @param  x   field base element.
             */
		std::ostream &write (std::ostream &os, Element x) const
            {
                return os << x;
            }

            /** Read field base element.
             * @pre This function assumes the field base element has already been
             * constructed and initialized.
             * @return input stream from which field base element is read.
             * @param  is  input stream from which field base element is read.
             * @param  x   field base element.
             */
		std::istream &read (std::istream &is, Element &x) const
            { is >> x; return is;
            }

            /** Read field base element.
             * @param is input stream
             * @param x
             * @return  \c is
             */
		std::istream &read (std::istream &is, BitVector::reference x) const
            { is >> x; return is;
            }

            /** Read field base element.
             * @param is input stream
             * @param x
             * @return  \c is
             */
		std::istream &read (std::istream &is, stdBitReference x) const
            {
                bool a = true;
                is >> a;
                x=a;
                return is;
            }

            //@}

            /** @name Arithmetic Operations
             * x <- y op z; x <- op y
             * These operations require all elements, including x, to be initialized
             * before the operation is called.  Uninitialized field base elements will
             * give undefined results.
             */
            //@{

            /** Addition.
             * x = y + z
             * This function assumes all the field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             * @param  z field base element.
             */
		Element &add (Element &x, Element y, Element z) const
            {
                return x = y ^ z;
            }

            /** Addition.
             * @param x
             * @param y
             * @param z
             */
		BitVector::reference add (BitVector::reference x, Element y, Element z) const
            {
                return x = y ^ z;
            }

            /** Addition.
             * @param x
             * @param y
             * @param z
             */
		stdBitReference add (stdBitReference x, Element y, Element z) const
            {
                return x = y ^ z;
            }

            /** Subtraction.
             * x = y - z
             * This function assumes all the field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             * @param  z field base element.
             */
		Element &sub (Element &x, Element y, Element z) const
            {
                return x = y ^ z;
            }

            /** Subtraction.
             * @param x
             * @param y
             * @param z
             */
		BitVector::reference sub (BitVector::reference x, Element y, Element z) const
            {
                return x = y ^ z;
            }

            /** Subtraction.
             * @param x
             * @param y
             * @param z
             */
		stdBitReference sub (stdBitReference x, Element y, Element z) const
            {
                return x = y ^ z;
            }

            /** Multiplication.
             * x = y * z
             * This function assumes all the field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             * @param  z field base element.
             */
		Element &mul (Element &x, Element y, Element z) const
            {
                return x = y & z;
            }

            /** Multiplication.
             * @param x
             * @param y
             * @param z
             */
		BitVector::reference mul (BitVector::reference x, Element y, Element z) const
            {
                return x = y & z;
            }

            /** Multiplication.
             * @param x
             * @param y
             * @param z
             */
		stdBitReference mul (stdBitReference x, Element y, Element z) const
            {
                return x = y & z;
            }

            /** Division.
             * x = y / z
             * This function assumes all the field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             * @param  z field base element.
             * @bug z is unused
             */
		Element &div (Element &x, Element y, Element z ) const
            {
                return x = y;
            }

            /** Division.
             * @param x
             * @param y
             * @param z
             */
		BitVector::reference div (BitVector::reference x, Element y, Element z ) const
            {
                return x = y;
            }

            /** Division.
             * @param x
             * @param y
             * @param z
             */
		stdBitReference div (stdBitReference x, Element y, Element z ) const
            {
                return x = y;
            }

            /** Additive Inverse (Negation).
             * x = - y
             * This function assumes both field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             */
		Element &neg (Element &x, Element y) const
            {
                return x = y;
            }

            /** Additive Inverse (Negation).
             * @return reference to x.
             * @param  x
             * @param  y
             */
		BitVector::reference neg (BitVector::reference x, Element y) const
            {
                return x = y;
            }

            /** Additive Inverse (Negation).
             * @return reference to x.
             * @param  x
             * @param  y
             */
		stdBitReference neg (stdBitReference x, Element y) const
            {
                return x = y;
            }

            /** Multiplicative Inverse.
             * x = 1 / y
             * This function assumes both field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             */
		Element &inv (Element &x, Element y) const
            {
                return x = y;
            }

            /** Multiplicative Inverse.
             * @return reference to x.
             * @param  x
             * @param  y
             */
		BitVector::reference inv (BitVector::reference x, Element y) const
            {
                return x = y;
            }

            /** Multiplicative Inverse.
             * @return reference to x.
             * @param  x
             * @param  y
             */
		stdBitReference inv (stdBitReference x, Element y) const
            {
                return x = y;
            }

            /** Natural AXPY.
             * r  = a * x + y
             * This function assumes all field elements have already been
             * constructed and initialized.
             * @return reference to r.
             * @param  r field element (reference returned).
             * @param  a field element.
             * @param  x field element.
             * @param  y field element.
             */
		BitVector::reference axpy (BitVector::reference r,
                                   Element a,
                                   Element x,
                                   Element y) const
            {
                return r = (a & x) ^ y;
            }

            /** Natural AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             * @param  y
             */
		stdBitReference axpy (stdBitReference r,
                              Element a,
                              Element x,
                              Element y) const
            {
                return r = (a & x) ^ y;
            }

            /** Natural AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             * @param  y
             */
		Element &axpy (Element &r, Element a, Element x, Element y) const
            {
                return r = (a & x) ^ y;
            }

            //@} Arithmetic Operations

            /** @name Inplace Arithmetic Operations
             * x <- x op y; x <- op x
             */
            //@{

            /** Inplace Addition.
             * x += y
             * This function assumes both field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             */
		Element &addin (Element &x, Element y) const
            {
                return x ^= y;
            }

            /** Inplace Addition.
             * @return reference to x.
             * @param  x
             * @param  y
             */
		BitVector::reference addin (BitVector::reference x, Element y) const
            {
                return x ^= y;
            }

            /** Inplace Addition.
             * @return reference to x.
             * @param  x
             * @param  y
             */
		stdBitReference addin (stdBitReference x, Element y) const
            {
                return x = x ^ y;
            }

            /** Inplace Subtraction.
             * x -= y
             * This function assumes both field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             */
		Element &subin (Element &x, Element y) const
            {
                return x ^= y;
            }

            /** Inplace Subtraction.
             * @return reference to x.
             * @param  x
             * @param  y
             */
		BitVector::reference subin (BitVector::reference x, Element y) const
            {
                return x ^= y;
            }

            /** Inplace Subtraction.
             * @return reference to x.
             * @param  x
             * @param  y
             */
		stdBitReference subin (stdBitReference x, Element y) const
            {
                return x = x ^ y;
            }

            /** Inplace Multiplication.
             * x *= y
             * This function assumes both field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             */
		Element &mulin (Element &x, Element y) const
            {
                return x &= y;
            }

            /** Inplace Multiplication.
             * @return reference to x.
             * @param  x
             * @param  y
             */
		BitVector::reference mulin (BitVector::reference x, Element y) const
            {
                return x &= y;
            }

            /** Inplace Multiplication.
             * @return reference to x.
             * @param  x
             * @param  y
             */
		stdBitReference mulin (stdBitReference x, Element y) const
            {
                return x = (bool)x & y;
            }

            /** Inplace Division.
             * x /= y
             * This function assumes both field base elements have already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             * @param  y field base element.
             * @bug y is unused
             */
		Element &divin (Element &x, Element y ) const
            {
                return x;
            }

            /** Inplace Division.
             * @return reference to x.
             * @param  x
             * @param  y
             * @bug y is unused
             */
		BitVector::reference divin (BitVector::reference x, Element y ) const
            {
                return x;
            }

            /** Inplace Division.
             * @return reference to x.
             * @param  x
             * @param  y
             * @bug y is unused
             */
		stdBitReference divin (stdBitReference x, Element y ) const
            {
                return x;
            }

            /** Inplace Additive Inverse (Inplace Negation).
             * x = - x
             * This function assumes the field base element has already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             */
		Element &negin (Element &x) const
            {
                return x;
            }

            /** Inplace Additive Inplace (Inplace Negation).
             * @return reference to x.
             * @param  x
             * @bug y is unused
             */
		BitVector::reference negin (BitVector::reference x) const
            {
                return x;
            }

            /** Inplace Additive Inplace (Inplace Negation).
             * @return reference to x.
             * @param  x
             * @bug y is unused
             */
		stdBitReference negin (stdBitReference x) const
            {
                return x;
            }

            /** Inplace Multiplicative Inverse.
             * x = 1 / x
             * This function assumes the field base elementhas already been
             * constructed and initialized.
             * @return reference to x.
             * @param  x field base element (reference returned).
             */
		Element &invin (Element &x) const
            {
                return x;
            }

            /** Inplace Multiplicative Inverse.
             * @return reference to x.
             * @param  x
             */
		BitVector::reference invin (BitVector::reference x) const
            {
                return x;
            }

            /** Inplace Multiplicative Inverse.
             * @return reference to x.
             * @param  x
             */
		stdBitReference invin (stdBitReference x) const
            {
                return x;
            }

            /** Inplace AXPY.
             * r  += a * x
             * This function assumes all field elements have already been
             * constructed and initialized.
             * Purely virtual
             * @return reference to r.
             * @param  r field element (reference returned).
             * @param  a field element.
             * @param  x field element.
             */
		Element &axpyin (Element &r, Element a, Element x) const
            {
                return r ^= a & x;
            }

            /** Inplace AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             */
		BitVector::reference axpyin (BitVector::reference r, Element a, Element x) const
            {
                return r ^= a & x;
            }

            /** Inplace AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             */
		stdBitReference axpyin (stdBitReference r, Element a, Element x) const
            {
                return r = r ^ (a & x);
            }

            /** Inplace AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             */
		Element &axpyin (Element &r, const stdBitReference a, Element x) const
            {
                return r ^= a & x;
            }

            /** Inplace AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             */
		stdBitReference axpyin (stdBitReference r, const stdBitReference a, Element x) const
            {
                return r = r ^ (a & x);
            }

            /** Inplace AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             */
		Element &axpyin (Element &r, Element a, const stdBitReference x) const
            {
                return r ^= a & static_cast<bool>(x);
            }

            /** Inplace AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             */
		stdBitReference axpyin (stdBitReference r, Element a, const stdBitReference x) const
            {
                return r = r ^ (a & static_cast<bool>(x));
            }

            /** Inplace AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             */
		Element &axpyin (Element &r, const stdBitReference a, const stdBitReference x) const
            {
                return r ^= a & static_cast<bool>(x);
            }

            /** Inplace AXPY.
             * @return reference to r.
             * @param  r
             * @param  a
             * @param  x
             */
		stdBitReference axpyin (stdBitReference r, const stdBitReference a, const stdBitReference x) const
            {
                return r = r ^ (a & static_cast<bool>(x));
            }

            //@} Inplace Arithmetic Operations

		static inline int maxCardinality()
            {
                return 2;
            }

	}; // class GF2

    template<>
    struct DenseVectorChooser<GF2> {
        typedef BitVector type;
    };

} // namespace LinBox

// #define LINBOX_field_gf2_H
// #include "linbox/vector/vector-domain.h"


// Specialization of homomorphism for basefield
#include "linbox/randiter/gf2.h"

#include <vector>

#include "linbox/field/gf2.inl"

#endif // __LINBOX_field_gf2_H

// Local Variables:
// mode: C++
// tab-width: 4
// indent-tabs-mode: nil
// c-basic-offset: 4
// End:
// vim:sts=4:sw=4:ts=4:et:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
